1. Field of the Invention
The present invention relates to a method of exposing resist on a photomask substrate used in the manufacture of semiconductor devices, and more particularly, to an exposing method for correcting a loading effect caused when a photomask substrate is dry-etched, and a recording medium formed according to the exposing method.
2. Description of the Related Art
A loading effect generally denotes a reduction in etch rate due to a shortage of an etch solution or etch gas which reacts with a substrate.
The types of loading effects include a micro loading effect and a macro loading effect. A micro loading effect denotes a variation in etch rate due to a failure in supplying an etch gas to a deep portion of an etch pattern as the aspect ratio of the etch pattern increases. A macro loading effect denotes a variation in etch rate with respect to the density of etch patterns formed on the periphery of another etch pattern.
According to the macro loading effect, when an electron beam resist film previously formed on a photomask substrate is removed, whether it is a positive- or negative-type film, the line width of an opaque layer below the electron beam resist film varies according to the density of an exposed area of the opaque layer (hereinafter, referred to as a xe2x80x9cloading densityxe2x80x9d) in a subsequent process for etching the opaque layer. The line width of a portion of the opaque layer having a high loading density is larger than that of a portion of the opaque layer having a low loading density. The above fact can be explained in terms of the etch rate of the opaque layer and the erosion rate of the electron beam resist film. In the high loading density region, the etch rate of the opaque layer decreases, but the erosion rate of the electron beam resist film increases, so that the line width increases compared to that in the low loading density region. Thus, the loading effect can vary depending on the material type of an electron beam resist film.
The line width variation due to the loading effect caused upon dry etching can be largely corrected by adjustment of an etching condition or by exposure with an additional compensation dose. A method of adjusting the etching conditions by additionally introducing a hydrochloric acid gas during dry etching has been suggested as an example of the former. However, this method is not an acceptable solution, since it causes generation of defects, distortion of line width and the like. An example of the latter, compensation dose, method is disclosed in Japanese Patent Publication No. Hei 10-10701. This method provides a correction dose upon exposure in order to obtain a desired pattern by experimentally obtaining the relationships between the line width difference and the correction exposure dose according to the density of the pattern (loading density) and by storing the obtained relationships in a database. However, a drawback with this approach is that it requires an excessive number of experiments in order to accumulate data on various-sized line widths of a desired pattern.
The present invention relates to a method of correcting the aforementioned macro loading effect caused by dry etching.
To address the above limitations of the conventional approaches, it is an object of the present invention to provide a method for correcting line width variation due to a loading effect by correction exposure.
Accordingly, to achieve the above object, there is provided a method of correcting a variation in line width due to a loading effect generated when the material layer on a photomask substrate is dry-etched to have a desired pattern, in which, first, a loading effect range xcex4 is obtained by dividing the substrate into meshes, and supposing the distribution of a loading effect frequency fL representing the degree of a loading effect at an arbitrary mesh on the substrate from each of the meshes to be a Gaussian distribution expressed in the following equation:             f      L        ⁢          (      r      )        =            k              π        ⁢                  xe2x80x83                ⁢                  δ          2                      ·          exp      ⁡              [                  -                      xe2x80x83                    ⁢                                    r              2                                      δ              2                                      ]            
wherein r denotes the distance between the arbitrary mesh and each of the other meshes, and k denotes a loading constant. Next, the loading density of the desired pattern, which is defined as a ratio of the area to be etched to the entire area in each mesh, is calculated. The loading effect at each of the meshes on the substrate can be calculated by convoluting the loading density of the desired pattern and the loading effect frequency obtained from the loading effect range. An electron beam resist is correction-exposed according to the loading effect calculated at each of the meshes on the substrate. In this way, a variation in line with is corrected. The loading effect L can be calculated from the following equation:       L    ⁢          (              x        ,        y            )        =            ∑              i        ,        j              ⁢                  D        ⁢                  (                      i            ,            j                    )                    ·              exp        ⁡                  [                      -                                                                                (                                          x                      -                      i                                        )                                    2                                +                                                      (                                          y                      -                      j                                        )                                    2                                                            δ                2                                              ]                    
wherein x,y denotes the coordinate of the arbitrary mesh, and D(i,j) denotes the loading density of the test patterns in a mesh having a coordinate (i,j).
The step of obtaining a loading effect range can include the step of forming test patterns by exposing, developing and etching a photomask substrate, and measuring the line width of the test pattern, and the step of calculating the loading effect expressed as the above-described equation an arbitrary loading effect range value, comparing the loading effects with the line widths of the test pattern at the meshes, and selecting a loading effect range in which the deviation between them is minimum. In the above equation, the loading density of test patterns is defined as a ratio of an area to be etched to the entire area of each mesh.
To achieve the second object, there is provided a recording medium readable by a computer which records a method of correcting a variation in line width. The recording medium includes a program module for obtaining a loading effect range xcex4 by dividing a predetermined pattern into meshes, calculating a loading effect L for each of the meshes with respect to arbitrary loading effect range values xcex4, and comparing the loading effect with a given line width, the loading effect L expressed as in the following equation:       L    ⁢          (              x        ,        y            )        =            ∑              i        ,        j              ⁢                  D        ⁢                  (                      i            ,            j                    )                    ·              exp        ⁡                  [                      -                                                                                (                                          x                      -                      i                                        )                                    2                                +                                                      (                                          y                      -                      j                                        )                                    2                                                            δ                2                                              ]                    
wherein x,y denotes the coordinate of an arbitrary mesh, and D(i,j) denotes the loading density of the patterns in a mesh having a coordinate (i,j).
The recording medium also includes a program module for calculating the loading density of the desired pattern, which is defined as a ratio of the area to be etched to the entire area of each mesh, a program module for receiving the loading effect range xcex4 and data of the loading density of the desired patterns and calculating the loading effect L of the desired pattern loaded on each of the meshes using the above equation for obtaining a loading effect, and a program module for calculating a correction-exposing dose for each of the meshes from the loading effect of the desired pattern.
According to the present invention, a line width variation due to a loading effect caused by the non-uniformity of a loading density can be reduced by a correction exposing method using a dose corresponding to a loading effect received from a desired pattern, the loading effect calculated from an equation expressed as the convolution of a Gaussian distribution and a loading density.
Also, the correction exposing method can be performed using a computer program, so that the calculation can be simply performed. Furthermore, the computer program can be loaded in exposing equipment, so that correction-exposing can be easily performed using the calculated values.